Fundamentals of Aerodynamics
6th Edition
ISBN: 9781259129919
Author: John D. Anderson Jr.
Publisher: McGraw-Hill Education
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Chapter 4, Problem 4.16P
For the conditions given in Problem 4.15, a more reasonable calculation of the skin friction coefficient would be to assume an initially laminar boundary layer starting at the leading edge. and then transitioning to a turbulent boundary layer at some point downstream. Calculate the skin-friction coefficient for the Spitfire’s airfoil described in Problem 4.15, but this time assuming a critical Reynolds number of
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Problem 1. A smooth plate with length L = 3.0 m and width b = 0.90 m moves through still air at STP at a velocity of
U = 4.5 m/s that is aligned with L. Calculate the following for a boundary layer that stays laminar and for one that
trips to turbulent at the leading edge: (a) boundary layer disturbance thickness, 8, at
x = 0.5, 1.0, 1.5, 2.0, 2.5, and 3.0 m from the leading edge of the plate, (b) wall shear stress, Tw, at those æ-
locations, and (c) friction drag, Fp.f, on one side of plate. (d) Calculate percent decrease in drag for laminar versus
turbulent boundary layer.
Compute the lift and drag coefficients for a symmetric, diamond-shaped airfoil with a
thickness-to-chord ratio t/c equal to 0.10, flying at Mach 3.5 in air (y=1.4) at zero angle of attack.
M₂ - 3.5
Consider the NACA 2412 airfoil, data for which is given in 4.10 and 4.11. The data are given for two values of the Reynolds number based on chord length. For the case where Rec = 3.1×106, estimate: (a) the laminar boundary layer thickness at the trailing edge for a chord length of 1.5 m and (b) the net laminar skin-friction drag coefficient for the airfoil.
Chapter 4 Solutions
Fundamentals of Aerodynamics
Ch. 4 - Consider the data for the NACA 2412 airfoil given...Ch. 4 - Consider an NACA 2412 airfoil with a 2-m chord in...Ch. 4 - Starting with the definition of circulation,...Ch. 4 - Starting with Equation (4.35), derive Equation...Ch. 4 - Consider a thin, symmetric airfoil at 1.5 angle of...Ch. 4 - The NACA 4412 airfoil has a mean camber line given...Ch. 4 - For the airfoil given in Problem 4.6, calculate...Ch. 4 - Compare the results of Problems 4.6 and 4.7 with...Ch. 4 - Starting with Equations (4.35) and (4.43), derive...Ch. 4 - For the NACA 2412 airfoil, the lift coefficient...
Ch. 4 - Consider again the NACA 2412 airfoil discussed in...Ch. 4 - For the airfoil in Problem 4.11, calculate the...Ch. 4 - In Section 3.15 we studied the case of the lifting...Ch. 4 - The question is often asked: Can an airfoil fly...Ch. 4 - The airfoil section of the wing of the British...Ch. 4 - For the conditions given in Problem 4.15, a more...
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- What happens if the required CL is larger than CLmax of your airfoil, and what speed regime is usually associated with that condition?arrow_forwardAircraft flying at an altitude of (3 Km) with a velocity of (100 m/sec). The planform area of the wing is (206 m² ). Find the overall drag force acting on this aircraft if you have the following data :- Aspect ratio= 10, Weight of the aircraft = 7.5 x 105 kg.m/s² Span efficiency factor = 0.95 Wing cross section is NACA 4412 airfoll Drag coefficient = 0.006arrow_forwardFor the NACA 2412 airfoil, the lift coefficient and moment coefficient about the quarter-chord at -6° angle of attack are -0.39 and -0.045, respectively. At 4° angle of attack, these coefficients are 0.65 and -0.037, respectively. Calculate the location of the aerodynamic center. -arrow_forward
- A closed-loop wind tunnel has a test section of cross-section W =3 ft by H =5 ft and length L =4 m. An aerofoil with 21% thickness to chord ratio and a chord length of 0.52 m is mounted vertically in the test section and spans the entire height. If the measured lift and drag coefficients are C; = 0.325 and Ca =0.0071, what is the lift coefficient after correcting for solid blockage, wake blockage and streamline curvature? Give your answer to 3 decimal places.arrow_forward6. For a wing of aspect ratio AR, having an elliptical lift distribution, the induced drag coefficient is (where CL is the lift coefficient) (b) TAR CL 2TAR (d) TAR2 (a) TAR 7. Laminar flow airfoil is used to reduce the (a) pressure drag (b) induced drag (c) skin friction drag (d) wave drag 8. Set the aerofoil your chosen angle of incidence is gives a good installed pressure distribution. (a) twelve degree (b) ten degree (c) eight degree 9. The critical Mach number for a thick airfoil will be (a) lesser than a thin airfoil. (b) greater than a thin airfoil. (c) equal to a thin airfoil. (d) cannot be related to thin airfoil 10. What is the dimension for Lift coefficient? (a) N/s (b) kg/N (c) Dimensionlessarrow_forwardA helicopter is hovering at an altitude where the density of air is 1.165 kg/m³. The helicopter rotor disc has a diameter of 9 m and is rotating at 466 rpm, with the blades having a chord of 0.16 m. Estimate the drag force in newtons per unit span along an elemental strip at the mid-span of the blade. You may assume the drag coefficient of the blade at the mid-span is 0.025.arrow_forward
- A NACA 2412 airfoil with a chord of 0.64m is flying in an airstream of standard sea level conditions. The freestream velocity is 70 m/s. Given the lift per unit span is 1,254 N/m. By using the experimental data for NACA 2412 data plot in Figure Q1c, investigatethe angle of attack of the airfoil and the analyze the value of drag per unit spanof the airfoil. Given that at standard sea level, ?=1.789×10-5 kg/m.s.arrow_forwardAir flows parallel to the surface of a smooth flat plate 10 m long. The boundary thickness at the leading edge. The Reynolds number at the trailing edge of the plate is 107. Calculate the total drag force due to skin friction on one side of the plate per unit width. Assume that for laminar boundary layer, up to Re, = 5 x 105, the skin friction coefficient is Gr 1.328(Re)-1/2 and for turbulent boundary layer 0.078(Re)-1/5. Take the density of air as 1.2 kg/m³ and Its dynamic viscosity as 1.8 x 10-5 kg/msarrow_forwardProblem 2 A Beechcraft Bonanza wing has the following dimensions: - chord = 1.4 m; - span (wing tip to wing tip) = 7m and - wing is roughly rectangular in shape. This plane is flying at 30 m/sec under standard sea level conditions. Model this wing as a flat plate for boundary layer analysis. a) Calculate the Reynolds number for the wing. b) Calculate the boundary layer thickness at the trailing edge of the wing assuming fully laminar flow. c) Calculate the boundary layer thickness at the trailing edge of the wing assuming fully turbulent flow. d) Calculate the skin friction drag on the full wing assuming laminar flow transitions to turbulent flow at a critical Reynolds number = 5.8 x 105.arrow_forward
- For a 10 deg included angle wedge at 0 deg AOA, calculate the lift and drag coefficient (Cl = 0, Cd = 0.082). Then calculate the lift and drag at AOA=4 deg (Cl = 0.16, Cd = 0.093). Let M=2.arrow_forwardCompute for the drag of a rectangular wing with a chord of 4.5 ft and a span of 16 ft. if the dynamic pressure 80 psi. Cd of the wing is 0.030.arrow_forwardThe lift curve for the 4 digit NACA 2421 airfoil is shown in the Figure. -Consider a wing with AR = 12, no sweep, and airplane flies at the Mach number equal to 0.65. The Oswald efficiency span number ?1 = 0.95 Calculate the lift slope for the finite wing. Clearly show the formula and explanations in the solution.arrow_forward
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